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Question

# The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure.Expenditure(in Rs.)FrequencyExpenditure(in Rs.)Frequency1000-1500243000-3500301500-2000403500-4000222000-2500334000-4500162500-3000284500-50007

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Solution

## Expenditure(in rupees)xiFrequency(fi) fixi 1000-1500 1250 2430000 1500-2000 1750 40 70000 2000-2500 2250 33 74250 2500-3000 2750 28 77000 3000-3500 3250 30 97500 3500-4000 3750 22 82500 4000-4500 4250 16 68000 4500-5000 4750 7 33250 Σfi=200 Σfixi=532500 Mean=ΣfixiΣfi=532500200=2662.5As frequency is maximum for the class 1500-2000, modal class is 1500−2000.Mode=l+f1−f02f1−(f0+f2)×hwhere,l = lower limit of modal class =1500f1 = frequency of modal class = 40f0 = frequency of class preceding the modal class = 24f2 = frequency of class succeding the modal class = 33h = higher limit - lower limit =2000−1500=500Mode=1500+40−242×40−(24+33)×500⇒mode=1500+1623×500=1500+347.83=1847.83Hence, the mean and modal monthly expenditure of the families are 2662.5 and 1847.83 respectively.

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